Group 6
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Group 6
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Assignment 1 - Select and Assess
Array Processing
Subject: Array Processing
Blaise Barney introduced Parallel Computing https://computing.llnl.gov/tutorials/parallel_comp/ Array processing could become one of the parallel example, which "demonstrates calculations on 2-dimensional array elements; a function is evaluated on each array element."
Here is my source code
| arrayProcessing.cpp |
|---|
// arrayProcessing.cpp
// Array processing implement parallel solution
#include <iostream>
#include <iomanip>
#include <cstdlib>
#include <ctime>
void init(float** randomValue, int n) {
//std::srand(std::time(nullptr));
float f = 1.0f / RAND_MAX;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
randomValue[i][j] = std::rand() * f;
}
void multiply(float** a, float** b, float** c, int n) {
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
float sum = 0.0f;
for (int k = 0; k < n; k++)
sum += a[i][k] * b[k][j];
c[i][j] = sum;
if(n <= 10){
std::cout << "array c[" << i << "," << j << "]: " << c[i][j] << std::endl;
}
}
}
int main(int argc, char* argv[]) {
// interpret command-line argument
if (argc != 2) {
std::cerr << argv[0] << ": invalid number of arguments\n";
std::cerr << "Usage: " << argv[0] << " size_of_matrices\n";
return 1;
}
int n = std::atoi(argv[1]); // size of matrices
float** a = new float*[n];
for (int i = 0; i < n; i++)
a[i] = new float[n];
float** b = new float*[n];
for (int i = 0; i < n; i++)
b[i] = new float[n];
float** c = new float*[n];
for (int i = 0; i < n; i++)
c[i] = new float[n];
std::srand(std::time(nullptr));
init(a, n);
init(b, n);
multiply(a, b, c, n);
for (int i = 0; i < n; i++)
delete [] a[i];
delete [] a;
for (int i = 0; i < n; i++)
delete [] b[i];
delete [] b;
for (int i = 0; i < n; i++)
delete [] c[i];
delete [] c;
}
|
Standard random method is used to initialize a 2-dimentional array. The purpose of this program is to perform a 2-dimension array calculation, which is a matrix-matrix multiplication in this example.
In this following profile example, n = 1000
Flat profile: Each sample counts as 0.01 seconds. % cumulative self self total time seconds seconds calls Ts/call Ts/call name 100.11 1.48 1.48 multiply(float**, float**, float**, int) 0.68 1.49 0.01 init(float**, int) 0.00 1.49 0.00 1 0.00 0.00 _GLOBAL__sub_I__Z4initPPfi
Call graph
granularity: each sample hit covers 2 byte(s) for 0.67% of 1.49 seconds
index % time self children called name
<spontaneous>
[1] 99.3 1.48 0.00 multiply(float**, float**, float**, int) [1]
-----------------------------------------------
<spontaneous>
[2] 0.7 0.01 0.00 init(float**, int) [2]
-----------------------------------------------
0.00 0.00 1/1 __libc_csu_init [16]
[10] 0.0 0.00 0.00 1 _GLOBAL__sub_I__Z4initPPfi [10]
-----------------------------------------------
�
Index by function name
[10] _GLOBAL__sub_I__Z4initPPfi (arrayProcessing.cpp) [2] init(float**, int) [1] multiply(float**, float**, float**, int)
From the call graph, multiply() took major runtime to more than 99%, as it contains 3 for-loop, which T(n) is O(n^3). Besides, init() also became the second busy one, which has a O(n^2).
As the calculation of elements is independent of one another - leads to an embarrassingly parallel solution. Arrays elements are evenly distributed so that each process owns a portion of the array (subarray). It can be solved in less time with multiple compute resources than with a single compute resource.
The Monte Carlo Simulation (PI Calculation)
Subject: The Monte Carlo Simulation (PI Calculation) Got the code from here: https://rosettacode.org/wiki/Monte_Carlo_methods#C.2B.2B A Monte Carlo Simulation is a way of approximating the value of a function where calculating the actual value is difficult or impossible.
It uses random sampling to define constraints on the value and then makes a sort of "best guess."
Zhijian
Subject:
